Basic topology & bevel help - How to fix beveling issue?
I've reworked your topology to get a more clean bevel, Try this:



By adding a little bit of thickness to the back face, you can allow more room for the bevel to run before it overshoots. But keep in mind there will always be artifacts if you push the bevel too far on any kind of geometry.
If you want a thicker bevel and more control over the mesh, you can always take a subd approach. But for this piece I don't think it's necessary.
Here's the blend file with the reworked topology:
https://blend-exchange.giantcowfilms.com/b/D2ZXy03E/
Hope this helps!